Question: Let A be a 4 x 4 marix and let he an eigenvalue of multiplicity 3. If A - l has rank 1. is

Let A be a 4 x 4 marix and let λ he an eigenvalue of multiplicity 3. If A - λl has rank 1. is A defective? Explain.

Step by Step Solution

★★★★★

3.45 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

If A I has rank 1 th... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

949-M-L-A-E (828).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

If A is a 4 4 matrix of rank 3 and = 0 is an eigenvalue of multiplicity 3, then A is diagonalizable. In the case of a true statement, explain or prove your answer. In the case of a false statement,...

Q:

If A is a 4 4 matrix of rank 1 and = 0 is an eigenvalue of multiplicity 3, then A is defective. In the case of a true statement, explain or prove your answer. In the case of a false statement, give...

Q:

Set A = ones(10) + eye(10) (a) What is the rank of A - I? Why must = 1 be an eigenvalue of multiplicity 9? Compute the trace of A using the MATLAB function trace. The remaining eigenvalue 10 must...

Q:

1. Let L(21, X2) = (2x1 + 5x2, 22, 21 - 242). Show that L a linear mapping and find its associated matrix. 2. Let A be the same matrix as in question 2 in Type C. a) Find a basis for the null space...

Q:

Can you please help me with number 12 and number 15. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! 5.7 Matrix Exponentials...

Q:

Can you please help me with number 12 and number 15. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! 5.6 Problems Find...

Q:

Can you please help me with number 21. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! Open with Chapter 5 Linear Systems...

Q:

Can you please help me with number 15. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! Linear Systems quations 406 The...

Q:

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Q:

Eigenvalue/Eigenvector Part IV: Suppose A is an n x n matrix. a. What does it mean to say that a vector x E Rn is an eigenvector of A? b. Suppose A E R is an eigenvalue of A. What is the eigenspace...

Q:

In an attempt to improve profit performance, Anderson Company's management is considering a number of alternative actions. An October contribution income statement for Anderson Company follows. Sales...

Q:

Find Laplace Transform Find laplace trns form f (t) = 3 2 f (t) = Sinht?(WE)

Q:

10. (Learning Objective 5) The triple bottom line focuses on a. profit. b. people. c. the planet. d. all of the above.

Q:

3. Consider two alternatives for Stromboli in 2011. In case (a), its inhabitants eat 60 million pizzas and build 6,000 pizza ovens. In case (b), the population eats 15 million pizzas but builds...

Q:

Let A and B be m n matrices. Show that A is row equivalent to B if and only if AT is column equivalent to BT.

Q:

Show that a square matrix which has a row or a column consisting entirely of zeros must be singular.

Q:

(a) Is (A + B)-1 = A-1 + B-1? (b) Is (cA)-1 = 1/c A-1?

Q:

Marianne Kramer, the owner of Handy Man Rentals, rents carpet cleaners to contractors and walk-in customers. She is interested in arriving at a forecast of rentals so that she can order the correct...

Q:

The null hypothesis says that a sprinter's reaction time follows a normal distribution with a mean at most 0.150 seconds. Six measurements of the sprinter's reaction time show...

Q:

You must evaluate the purchase of a proposed spectrometer for the R&D department. The purchase price of the spectrometer including modifications is $170,000, and the equipment will be fully...